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音乐乐谱中的多重标度行为和非线性特征。

Multiple scaling behaviour and nonlinear traits in music scores.

作者信息

González-Espinoza Alfredo, Larralde Hernán, Martínez-Mekler Gustavo, Müller Markus

机构信息

Instituto de Investigación en Ciencias Básicas y Aplicadas, UAEM, Morelos, México.

Instituto de Ciencias Físicas, UNAM, Morelos, México.

出版信息

R Soc Open Sci. 2017 Dec 13;4(12):171282. doi: 10.1098/rsos.171282. eCollection 2017 Dec.

DOI:10.1098/rsos.171282
PMID:29308256
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC5750023/
Abstract

We present a statistical analysis of music scores from different composers using detrended fluctuation analysis (DFA). We find different fluctuation profiles that correspond to distinct autocorrelation structures of the musical pieces. Further, we reveal evidence for the presence of nonlinear autocorrelations by estimating the DFA of the magnitude series, a result validated by a corresponding study of appropriate surrogate data. The amount and the character of nonlinear correlations vary from one composer to another. Finally, we performed a simple experiment in order to evaluate the pleasantness of the musical surrogate pieces in comparison with the original music and find that nonlinear correlations could play an important role in the aesthetic perception of a musical piece.

摘要

我们使用去趋势波动分析（DFA）对不同作曲家的音乐乐谱进行了统计分析。我们发现了与音乐作品不同自相关结构相对应的不同波动谱。此外，通过估计幅度序列的DFA，我们揭示了存在非线性自相关的证据，这一结果通过对适当替代数据的相应研究得到了验证。非线性相关性的数量和特征因作曲家而异。最后，我们进行了一个简单的实验，以评估音乐替代作品与原始音乐相比的愉悦程度，发现非线性相关性可能在音乐作品的审美感知中发挥重要作用。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/f43e/5750023/7196702917cd/rsos171282-g14.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/f43e/5750023/abf0cb651b26/rsos171282-g7.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/f43e/5750023/15fc7a48b2d4/rsos171282-g8.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/f43e/5750023/128d81aa0643/rsos171282-g10.jpg
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